# Temperature

The temperature of a system in classical thermodynamics is intimately related to the zeroth law of thermodynamics; two systems having to have the same temperature if they are to be in thermal equilibrium (i.e. there is no net heat flow between them). However, it is most useful to have a temperature scale. By making use of the ideal gas law one can define an absolute temperature

$T = \frac{pV}{Nk_B}$

however, perhaps a better definition of temperature is

$\frac{1}{T(E,V,N)} = \left. \frac{\partial S}{\partial E}\right\vert_{V,N}$

where S is the entropy.

Temperature has the SI units of kelvin (K) (named in honour of William Thomson ) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water .

$T = \frac{2}{3} \frac{1}{k_B} \overline {\left(\frac{1}{2}m_i v_i^2\right)}$

where kB is the Boltzmann constant. The kinematic temperature so defined is related to the equipartition theorem.

## References

1. William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine October pp. (1848)
2. H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia 27 pp. 3-10 (1990)
3. H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia 27 p. 107 (1990)
4. Hans Henrik Rugh "Dynamical Approach to Temperature", Physical Review Letters 78 pp. 772-774 (1997)
5. András Baranyai "On the configurational temperature of simple fluids", Journal of Chemical Physics 112 pp. 3964-3966 (2000)
6. Alexander V. Popov and Rigoberto Hernandez "Ontology of temperature in nonequilibrium systems", Journal of Chemical Physics 126 244506 (2007)
7. J.-L. Garden, J. Richard, and H. Guillou "Temperature of systems out of thermodynamic equilibrium", Journal of Chemical Physics 129 044508 (2008)